Question

Using the truth table, state whether the following proposition is a tautology, contingency or a contradiction :

3 ~ (A ∧ B) V (~ A ⇒ B)

Answer 1

A	B	A ∧ B	~ (A ∧ B)	~ A	~A ⇒ B
0	0	0	1	1	0
0	1	0	1	1	1
1	0	0	1	0	1
1	1	1	0	0	1

~ (A ∧ B) ∨ (~ A ⇒ B) have all 1's, therefore Proposition is a tautology.